The definition of the positive definite(PD) of the matrix(H) is v’*H*v>0 for all non zero vector. The inner product between the vector is proportional to cosine of the angle between the vectors. If we consider v’*(H*v)>0 means the angle between the vector v and H*v(transformed vector) is acute.So positive definite matrix is not going to transforms vector >90 degrees.In the quasi-newton method the condition says that the transforming matrix should be positive definite.The reason for this that the matrix changes the gradient direction,If it is not PD,then the direction of the movement will be obtuse with the gradient(maximum local decent) and that will not be the decent direction…

-Achuth